Problem 92 - Chemistry The Central Science In Si Units

Question

A standard air conditioner involves a refrigerant that is typically now a fluorinated hydrocarbon, such as \(\mathrm{CH}_{2} \mathrm{~F}_{2}\). An air- conditioner refrigerant has the property that it readily vaporizes at atmospheric pressure and is easily compressed to its liquid phase under increased pressure. The operation of an air conditioner can be thought of as a closed system made up of the refrigerant going through the two stages shown here (the air circulation is not shown in this diagram). During expansion, the liquid refrigerant is released into an expansion chamber at low pressure, where it vaporizes. The vapor then undergoes compression at high pressure back to its liquid phase in a compression chamber. (a) What is the sign of \(q\) for the expansion? (b) What is the sign of \(q\) for the compression? (c) In a central air-conditioning system, one chamber is inside the home and the other is outside. Which chamber is where, and why? (d) Imagine that a sample of liquid refrigerant undergoes expansion followed by compression, so that it is back to its original state. Would you expect that to be a reversible process? (e) Suppose that a house and its exterior are both initially at \(31^{\circ} \mathrm{C}\). Some time after the air conditioner is turned on, the house is cooled to \(24^{\circ} \mathrm{C}\). Is this process spontaneous or nonspontaneous?

Step-by-Step Solution

Answer

(a) Positive; (b) Negative; (c) Expansion inside, compression outside; (d) Irreversible; (e) Non-spontaneous.

Step 1: Understanding the Expansion Process

During the expansion phase of the air conditioner cycle, the liquid refrigerant is released into an expansion chamber where it vaporizes under low pressure. Since this is an endothermic process, the system absorbs heat from its surroundings, making the sign of \( q \) for the expansion process positive.

Step 2: Analyzing the Compression Process

In the compression phase, the vaporized refrigerant is compressed at high pressure back to a liquid. This process releases heat to the surroundings, making it an exothermic process. Therefore, the sign of \( q \) for the compression is negative.

Step 3: Identifying Chamber Locations

In a central air-conditioning system, the expansion chamber is located inside the home because it absorbs heat from the indoor air to vaporize the refrigerant. Meanwhile, the compression chamber is located outside the home as it releases the absorbed heat to the exterior.

Step 4: Evaluating Process Reversibility

A reversible process is one where the system and its surroundings can be returned to their original states without any changes. Since the refrigerant undergoes expansion followed by compression and eventually returns to its initial state, this might be viewed as a reversible process. However, in practice, it involves irreversible factors such as friction and non-equilibrium states, making it practically irreversible.

Step 5: Determining Process Spontaneity

In thermodynamics, a spontaneous process is one that occurs naturally without external intervention. The air conditioning process cools the house from \(31^{\circ}\mathrm{C}\) to \(24^{\circ}\mathrm{C}\), making it a non-spontaneous process because it requires the air conditioner to work actively against the natural tendency for systems to achieve thermal equilibrium.

Key Concepts

Endothermic and Exothermic Processes

In thermodynamics, processes are often described as either endothermic or exothermic based on how they interact with heat. This is crucial in understanding refrigeration systems, like those in air conditioners. When we say a process is endothermic, it means it absorbs heat. Expansion of refrigerants within an air conditioner is endothermic. As the refrigerant transitions from a liquid to a gaseous state in the expansion chamber, it draws in heat from the surrounding environment.
This absorption of heat makes the surroundings cooler, which is the primary cooling action of the air conditioner.
In contrast, an exothermic process releases heat. During the compression phase, the refrigerant is turned back into a liquid from a gas, releasing the heat it previously absorbed. This heat is expelled to the surroundings, often outside the house, allowing the building to cool down.
This basic understanding of heat exchange processes helps illustrate why the sign of heat (q) is positive during expansion and negative during compression.

• Endothermic: absorbs heat, positive q.
• Exothermic: releases heat, negative q.

Reversibility in Thermodynamic Systems

Thermodynamic processes are often analyzed in terms of reversibility. A reversible process is ideal—it completely reverses without leaving any change in the system or surroundings.
However, real-world systems are seldom perfectly reversible. In refrigeration, while theoretically, one might consider the cycle of refrigerant returning to its original state as reversible, practical factors suggest otherwise.
Imperfections such as friction, non-equilibrium states, and energy losses render most processes irreversible.
Despite the refrigerant undergoing a full cycle of expansion and compression, it encounters practical inefficiencies. These inefficiencies arise due to limitations in machinery, resulting in the process being irreversible.

• A reversible process: Ideal, no net changes.
• Real-world refrigeration: Inefficiencies make them irreversible.

Spontaneity in Thermodynamic Processes

Spontaneity in thermodynamics refers to whether a process occurs naturally without added energy. Spontaneous processes align with nature's tendency to reach a state of equilibrium or maximum entropy.
In the context of air conditioning, cooling a house from a higher temperature to a lower one isn't spontaneous. This action requires active energy input from the air conditioning unit to achieve the desired temperature inside the home.
Without the intervention of the air conditioner, the natural tendency would be for the house to remain at a higher temperature or even increase due to external heat sources.
This dependence on the air conditioner reveals the non-spontaneous nature of the process. It works against natural entropy, necessitating the continuous input of energy to cool the interior of the house below the ambient temperature.

• Spontaneity: Natural tendency towards equilibrium.
• Non-spontaneous processes: Require energy to occur (like cooling a house).